I have the same behaviour on a Sony Z3 Compact tablet.
As far as I understand it, the change is not saved and therfore davdroid can not do anything at all
nethertheless I hope that somebody has a hint for my there I have to look to solve this problem.
A different contact app can not solve the problem (like true contacts) because they all use the same apps in the background which manage the contacts.@zoulhh could your solve your issue and if yes how?